EFFECTS OF CHANGES OF BIRTH AND DEATH RATES 669 The ideal study would consider all of these elements not for a cross section in time, but following groups of individual women of the same age as they go through reproduction. Such cohorts, as they are called, have different characteristics from cross sections; in particular total fertility and mortality are more constant from one cohort to another than from one period to another. Ryder has made careful studies of the nature of cohort fertility and the distortions it undergoes when translated into period terms (10, and elsewhere). High Fertility and Low Crude Death Rates Whereas lower death rates can make a population younger or older, higher birth rates act more simply on age-distribution-they can only make it younger. Because of this fact, the lowest crude death rates in the world today are not shown by the United States and Europe but by Ceylon (7.51 per 1,000 in 1967), Taiwan (5.36 per 1,000 in 1966), and Hong Kong (5.01 per 1,000 in 1966). The United States rate was 9.36 per 1,000 in 1967, and the aggregate of Europe was 10.20 in 1965. Poor countries are tending to have lower crude death rates than rich ones. A way of showing this by demographic data alone is in terms of standardized rates. The directly standardized death rate on the United States 1960 population tells us what overall death rate would apply in various countries if their age-sex distribution were that of the United States in 1960. By holding constant age and sex we attain an index of mortality, or one might say of unhealthfulness, presumably directly related to poverty. The selected countries charted in Figure 2, including some rich and some poor, show a general inverse relation between crude and standardized rates. The Two-Sex Model We now incorporate sex in the model, but drop age. If the number of males at time t is M(t), their birth rate bm, and their death rate dm , and the corresponding symbols for females are F(t), bj- and d^, then we have the equations due to Goodman (11) M'(t) = -dmM(i) + bmF(t), F'(t) = -dfF(t)as so drastic an effect that we find A-N-P below the simple age-intrinsic rateA In short, the effect of nuptiality more than offsets the effect of simple parity. Whelpton (8) did the basic work on parity, and Karmel (9) suggested the importance of nuptiality. Oechsli's (7) recent calculations show the importance of both.